About Doob's inequality, entropy and Tchebichef

Abstract : In this paper we give upper bounds on the tail or the quantiles of the one-sided maximum of a nonnegative submartingale in the class L log L or the maximum of a submartingale in L^p. Our upper bounds involve the entropy in the case of nonnegative martingales in the class L log L and the L^p-norm in the case of submartingales in L^p. Starting from our results on entropy, we also improve the so-called bounded differences inequality. All the results are based on optimal bounds for the conditional value at risk of real-valued random variables.
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https://hal.archives-ouvertes.fr/hal-01630272
Contributor : Emmanuel Rio <>
Submitted on : Tuesday, November 7, 2017 - 2:00:23 PM
Last modification on : Thursday, July 18, 2019 - 11:26:01 AM
Long-term archiving on : Thursday, February 8, 2018 - 2:11:41 PM

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Emmanuel Rio. About Doob's inequality, entropy and Tchebichef. 2017. ⟨hal-01630272⟩

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